The UPDATE command looks ok, if there is a valid Contact ID in your text box, and no special characters - a single space is all it would take to cause a problem. I would suggest that you use Parametrized queries anyway: they are a lot safer, and make your code easier to read:
string strUpdate = "UPDATE Contact SET ContactLastName = @CLN WHERE ContactId = @CID";
OleDbCommand cmd = new OleDbCommand(strUpdate, conn);
cmd.Parameters.AddWithValue("@CLN", txtLastName.Text);
cmd.Parameters.AddWithValue("@CID", txtContactId.Text);
This may well get rid of your error!